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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.3, Problem 52E

To determine

The value of *v* which minimizes the total energy required to swim a fixed distance.

Expert Solution

The value of *v* which minimizes the total energy is 7.5mi/h.

**Given:**

The total energy required to swim a distance of 10 mi against a current of 5 mi/h is given by,

**Calculation:**

Use a graphing calculator to draw the graph of the function *E* with respect to *v* as shown in Figure 1.

Figure (1)

Locate the point at which local minimum occurs to find the value of *v* which minimizes the total energy.

The value
*b* is near *v*.

From Figure (1), it is noticed that there is one local minimum between

Point

The value 4606.875 is minimum for

Therefore, the value of *v* which minimizes the total energy is 7.5mi/h.